ScholarLens Back to search
2010•Unpublished venueRequires access

Minimal residual methods for solving a class of R-linear systems of equations

Kui Du, Olavi Nevanlinna

Open publisher page 2 citations

Abstract

Recently, R-linear GMRES was proposed by Eirola, Huhtanen and von Pfaler [SIAM J. Matrix Anal. Appl. 25 (2004), pp. 804–828] for solving a class of R-linear systems of equations. In this work we investigate R-linear GMRES through the equivalent real formulations of the R-linear system. We show that R-linear GMRES requires fewer matrix-vector products than GMRES applied to the related C-linear system. Numerical results for an artificial example and the inverse problem of reconstructing an unknown electric conductivity are reported to confirm our theoretical results. AMS subject classifications: 65F10, 15A18

About this research paper

What this paper is about

Recently, R-linear GMRES was proposed by Eirola, Huhtanen and von Pfaler [SIAM J. Matrix Anal. Appl. 25 (2004), pp. 804–828] for solving a class of R-linear systems of equations. In this work we investigate R-linear GMRES through the equivalent real formulations of the R-linear system. We show that R-linear GMRES requires fewer matrix-vector products than GMRES applied to the related C-linear system. Numerical results for an artificial example and the inverse problem of reconstructing an unknown electric conductivity are reported to confirm our theoretical results. AMS subject classifications: 65F10, 15A18

Why it matters

OpenAlex reports 2 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Recently, R-linear GMRES was proposed by Eirola, Huhtanen and von Pfaler [SIAM J. Matrix Anal. Appl. 25 (2004), pp. 804–828] for solving a class of R-linear systems of equations. In this work we investigate R-linear GMRES through the equivalent real formulations of the R-linear system. We show that R-linear GMRES requires fewer matrix-vector products than GMRES applied to the related C-linear system. Numerical results for an artificial example and the inverse problem of reconstructing an unknown electric conductivity are reported to confirm our theoretical results. AMS subject classifications: 65F10, 15A18

Key concepts: Generalized minimal residual method, Linear system, Mathematics, System of linear equations, Coefficient matrix, Applied mathematics, Linear equation, Matrix (chemical analysis)

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
Minimal residual methods for solving a class of R-linear systems of equations — Research Paper | ScholarLens